Efficiency Control Via Watt Control Via Duty Cycle Control Without Motor KV Knowledge?Where:

K= 90% = Desired Electrical to Mechanical Conversion Efficiency Setting

L= 500w = Desired Minimum Available Wattage Setting

P= 2000w = Desired Maximum Available Wattage Setting&

P>=LG= 50V = Pack Voltage

F= 0.1ohm = Winding Resistance

I= 100kv = Motor KV

J= 2200rpm = Present RPM

D= 22V = Present Back Emf V

M= 100% = Throttle Setting

A= XX.XXXA = Battery Amps

B= XX.XXXA = Motor Amps

C= XX.XXX% = Duty Cycle

E= XX.XXXV = Effective PWM Voltage

H= XX.XXXw = Throttled Wattage

N= XX.XXXw = Full Throttle Wattage

D=(1/I)*J <---------Calculating Back EMF Voltage from Motor KV and Present RPM

&

E=D/(K/100) <---------Calculating Effective PWM Voltage from Present Back EMF Voltage and Desired Efficiency Setting

^If Back EMF V is known -

Motor KV & RPM knowledge is not necessary&

if E>G then E=G <---------Ensuring Effective PWM Voltage is less than or equal to Battery Pack Voltage

&

if E>(G*(0.95)) then E=(G*(0.95)) <---------(Optional) Ensuring Effective PWM Voltage results in duty cycle less than or equal to VESC max duty cycle 95%

&

C=(E/G)*100 <---------Calculating Duty Cycle % from Effective PWM Voltage and Pack Voltage

&

B=(E-D)/F <---------Motor Amps From Effective PWM Voltage, Present Back EMF Voltage & Winding Resistance

&

A=B*(C/100) <---------Calculating Battery Amps from Motor Amps and Duty Cycle

&

N=A*G <---------Calculating Full Throttle Desired Wattage from Battery Amps and Pack Voltage

&

if N<L then N=L <---------Ensuring Full Throttle Desired Efficiency Wattage is greater than or equal to Minimum Wattage Setting

&

if N>P then N=P <---------Ensuring Full Throttle Desired Efficiency Wattage is less than or equal to Maximum Wattage Setting

&

H=N*(M/100) <---------Calculating Desired Wattage From Throttle Position and Full Throttle Desired Wattage

&

A=H/G <---------Re-calculating Battery Amps From Desired Wattage and Pack Voltage

&

E=(1/2)(sqrt((4*A*F*G)+D^2)+D) <---------Re-calculating Effective PWM Voltage From Battery Amps, Winding Resistance, Pack Voltage & Present Back EMF

&

C=(E/G)*100 <---------Re-calculating Duty Cycle % from Effective PWM Voltage & Pack Voltage

&

B=A/(C/100) <---------Re-calculating Motor Amps from Battery Amps & Duty Cycle

&

repeat

therefore:

K= 90% = Desired Efficiency SettingL= 500w = Desired Minimum Available Wattage Setting

P= 2000w = Desired Maximum Available Wattage Setting

G= 50V = Pack Voltage

F= 0.1ohm = Winding Resistance

I= 100kv = Motor KV

J= 2200rpm = Present RPM

D= 22V = Present Back Emf V

M= 100% = Throttle Setting

A= 11.95061A = Battery Amps

B= 24.44444A = Motor Amps

C= 48.88888% = Duty CycleE= 24.44444V = Effective PWM Voltage

H= 597.5305w = Throttled Wattage

N= 597.5305w = Full Throttle Wattage

&

597.5305W Electrical = 11.95061 battery amps * 50V

<-------- 597.5305W Electrical In537.78673w = 2.33419Nm*2200rpm/9.5488

<------ 537.78673W Mechanical Output @ 2200rpm @ 24.44444V Effective Volts @ 100kv @ 0.1ohm

(537.78673W/597.5305W)*100=90.00% <----------- 90.00% conversion efficiency of electrical to mechanical watts.proof:

1/100=0.01 volts per rpm <---- simply 100 rpm per volt is 0.01 volts per rpm

2200rpm*0.01v=22V <---- 22V present back emf voltage at 2200rpm

24.44444V-22V=2.44444V <------- Effective Voltage minus back emf voltage equals 2.44444 net volts

24.44444A=2.44444V/0.1ohm <---- 24.44444A Motor Amps @ 2200rpm

100kv*2=200

200*pi=628.3185

628.3185/60=10.4719r/vs <-------------- 100kv is 10.4719 radians per second per volt

0.09549=1/10.4719 <--------100kv = 0.09549Nm/A

24.44444A Motor Amps * 0.09549NM/A = 2.33419Nm <----- 2.33419 Newton Meters Torque at 24.44444A Motor Amps

537.78673w = 2.33419Nm*2200rpm/9.5488 <------ 537.78673W Mechanical Output @ 2200rpm @ 24.44444V Effective Volts @ 100kv @ 0.1ohm

Assuming 50V battery pacK

(24.44444V Effective V/50V Pack V)*100= 48.88888% duty cycle <------------ 24.44444V Effective Volts is 48.88888% duty cycle w/ 50V Battery Pack

&:

Battery Amps = Motor Amps x (Duty Cycle/100)

therefore:

11.95061 battery amps = 24.44444 motor amps * (%48.88888 duty cycle/100) <------------ 24.44444 motor amps @ 48.88888% duty cycle is 11.95061 battery amps

597.5305W Electrical = 11.95061 battery amps * 50V <-------- 597.5305W Electrical In

537.78673w = 2.33419Nm*2200rpm/9.5488 <------ 537.78673W Mechanical Output @ 2200rpm @ 24.44444V Effective Volts @ 100kv @ 0.1ohm

(537.78673W/597.5305W)*100=90.00% <----------- 90.00% conversion efficiency of electrical to mechanical watts.---------------

Simply in theory,

without knowing the motor's KV or rpm, it should still be possible to implement efficiency control based only on Back EMF readings, possibly by utilizing watt control via duty cycle control.